A 25 ft ladder is leaning against a vertical wall. At what rate (with respect to time) is the angle theta between the ground and the ladder changing, if the top of the ladder is sliding down the wall at the rate of r inches per second, at the moment that the top of the ladder is h feet from the ground? (You're looking here for an equation in terms of h and theta.)

Question

A 25 ft ladder is leaning against a vertical wall. At what rate (with respect to time) is the angle theta between the ground and the ladder changing, if the top of the ladder is sliding down the wall at the rate of r inches per second, at the moment that the top of the ladder is h feet from the ground? (You're looking here for an equation in terms of h and theta.)
You can find a visual on Chegg by searching the question.

Please help ASAP.

mathhelper · Answer

Your sketch should consist of a right-angled triangle.
Hypotenuse = 25 and height = h
angle ladder makes with ground = θ

The given units refer to hypotenuse and opposite side, so
we'll go for sinθ
sinθ = h/25
25sinθ = h
25 cosθ dθ/dt = dh/dt , but we are given that dh/dt = -r inches/s = -r/12 ft/s
dθ/dt = (-r/12)/(25cosθ) = -r/(300cosθ) radians/s

Miller · Answer

Please look at the first visual from the Chegg website, by searching this question: Which option do u think is correct?